We present and compare learning rate schedules for stochastic gradient descent, a general algorithm which includes LMS, online backpropagation andk-means clustering as special cases. We introduce "search-thenconverge" typeschedules which outperform the classical constant and "running average" (1ft) schedules both in speed of convergence and quality of solution.

A Boltzmann machine ([AHS], [HS], [AK]) is a neural network model in which the units update their states according to a stochastic decision rule. It consists of a set U of units, a set C of unordered pairs of elements of U, and an assignment of connection strengths S: C -- R. A configuration of a Boltzmann machine is a map k: U -- {O, I}.

Padhraic Smyth Communications Systems Research Jet Propulsion Laboratory California Institute of Technology Pasadena, CA 91109 Abstract Given some training data how should we choose a particular network classifier froma family of networks of different complexities? In this paper we discuss how the application of stochastic complexity theory to classifier design problems can provide some insights into this problem. In particular we introduce the notion of admissible models whereby the complexity of models under consideration is affected by (among other factors) the class entropy, the amount of training data, and our prior belief. In particular we discuss the implications of these results with respect to neural architectures anddemonstrate the approach on real data from a medical diagnosis task. 1 Introduction and Motivation In this paper we examine in a general sense the application of Minimum Description Length (MDL) techniques to the problem of selecting a good classifier from a large set of candidate models or hypotheses. Pattern recognition algorithms differ from more conventional statistical modeling techniques in the sense that they typically choose from a very large number of candidate models to describe the available data.

Terrence L. Fine School of Electrical Engineering Cornell University Ithaca, NY 14853 Abstract The three problems that concern us are identifying a natural domain of pattern classification applications of feed forward neural networks, selecting anappropriate feedforward network architecture, and assessing the tradeoff between network complexity, training set size, and statistical reliability asmeasured by the probability of incorrect classification. We close with some suggestions, for improving the bounds that come from Vapnik Chervonenkis theory, that can narrow, but not close, the chasm between theory and practice. Neural networks are appropriate as pattern classifiers when the pattern sources are ones of which we have little understanding, beyond perhaps a nonparametric statistical model, but we have been provided with classified samples of features drawn from each of the pattern categories. Neural networks should be able to provide rapid and reliable computation of complex decision functions. The issue in doubt is their statistical response to new inputs.

Learning can increase the rate of evolution of a population of biological organisms (the Baldwin effect). Our simulations show that in a population of artificial neural networks solving a pattern recognition problem, no learning or too much learning leads to slow evolution of the genes whereas an intermediate amount is optimal. Moreover, for a given total number of training presentations, fastest evoution occurs if different individuals within each generation receive different numbers of presentations, rather than equal numbers. Because genetic algorithms (GAs) help avoid local minima in energy functions, our hybrid learning-GA systems can be applied successfully to complex, highdimensional patternrecognition problems. INTRODUCTION The structure and function of a biological network derives from both its evolutionary precursors and real-time learning.

Feature selection and creation are two of the most important and difficult tasks in the field of pattern classification. Good features improve the performance of both conventional and neural network pattern classifiers. Exemplar selection is another task that can reduce the memory and computation requirements of a KNN classifier. These three tasks require a search through a space which is typically so large that 797 798 Chang and Lippmann exhaustive search is impractical. The purpose of this research was to explore the usefulness of Genetic search algorithms for these tasks. Details concerning this research are available in (Chang, 1990).

We describe a recurrent connectionist network, called CONCERT, that uses a set of melodies written in a given style to compose new melodies in that style. CONCERT is an extension of a traditional algorithmic composition technique inwhich transition tables specify the probability of the next note as a function of previous context. A central ingredient of CONCERT is the use of a psychologically-grounded representation of pitch.

We compare the performance of the modular architecture, composed of competing expert networks, suggested by Jacobs, Jordan, Nowlan and Hinton (1991) to the performance of a single back-propagation network on a complex, but low-dimensional, vowel recognition task. Simulations reveal that this system is capable of uncovering interesting decompositions in a complex task. The type of decomposition is strongly influenced by the nature of the input to the gating network that decides which expert to use for each case. The modular architecture also exhibits consistently better generalization on many variations of the task. 1 Introduction If back-propagation is used to train a single, multilayer network to perform different subtasks on different occasions, there will generally be strong interference effects which lead to slow learning and poor generalization. If we know in advance that a set of training cases may be naturally divideJ into subsets that correspond to distinct subtasks, interference can be reduced by using a system (see Figure 1) composed of several different "expert" networks plus a gating network that decides which of the experts should be used for each training case. Systems of this type have been suggested by a number of authors (Hampshire and Waibel, 1989; Jacobs, Jordan and Barto, 1990; Jacobs et al., 1991) (see also the paper by Jacobs and Jordan in this volume (1991».

Omohundro ICSI 1947 Center St., Suite 600 Berkeley, CA 94704 We identify the three principle factors affecting the performance of learning bynetworks with localized units: unit noise, sample density, and the structure of the target function. We then analyze the effect of unit receptive fieldparameters on these factors and use this analysis to propose a new learning algorithm which dynamically alters receptive field properties during learning.

Bruno Caprile I.R.S.T. Povo, Italy, 38050 Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function.